1. Introduction

Optically anisotropic materials are integral for applications in polarization control [1–3], phase-matching [4,5], and imaging [6,7]. These materials’ ability to shape the propagation of light stems from their birefringence (Δn), which is the difference between the refractive indices of a material’s principal axes. Birefringence has been observed in intrinsic inorganic crystals like calcite and rutile titania (TiO₂) [8–11], liquid crystals and other elongated molecules [12–15], and is the basis of birefringent nanophotonic structures used in optical antennas and metasurfaces [16–20]. While birefringent materials have been integrated into many planar elements for polarization control, the processing challenges associated with each material make it difficult to extend their use to anisotropic lensing and beam-shaping applications. Inorganic crystals for instance require precise alignment of the optical axis and complicated processing to impart geometric features like curvature [21,22]. Liquid crystals provide excellent polarization control, but often exhibit lower birefringence (Δn < 0.2) [23]. Metasurfaces and other nanophotonic elements are often made from lossy materials and are functionally limited to narrow bandwidths [24–26].

Structured nanocomposites are another type of birefringent material that derive their anisotropy from nanoscale inclusions of a secondary material [17,27,28]. Porous silicon (PSi) and porous silicon oxide (PSiO₂) are mesoporous composites with birefringence stemming from their highly anisotropic pore structure [29–33]. PSi is formed by electrochemically porosifying bulk silicon, and can be subsequently thermally oxidized to form porous silicon dioxide (PSiO₂) [29,34–36]. The PSi and PSiO₂ refractive index (determined by porosity) can be spatially varied during the initial electrochemical etch process, allowing the formation of gradient refractive index (GRIN) elements [34,37,38]. PSi’s birefringence also changes with porosity and can attain values larger than 0.3 at visible frequencies [31,32,39], enabling its use in polarization-sensitive elements like birefringent spectral filters and dielectric mirrors [40,41]. Additionally, PSi GRIN lenses have been shown to exhibit polarization selective focusing behavior; depending on the polarization state of the illuminating beam, the lens will either produce a single focus or will split the beam into two foci [38]. Due to the complex, porosity-dependent birefringence of a PSi GRIN profile, predicting these lenses’ birefringent focal response is difficult without a thorough understanding of the material’s optical anisotropy.

In this work, we correlate these GRIN lenses’ polarization selective focal response with the birefringence profiles accessible to these porous materials. Lithographically shaped, 20-µm square GRIN optics were fabricated from PSi, PSiO₂, and PSiO₂/TiO₂. These elements demonstrate unique polarization-selective behavior that is enabled by the spatially varying birefringence that is supported by these structurally anisotropic materials. By keeping the magnitude of the range (n_edge to n_center) of the refractive index profile constant while changing the birefringence profile, we show that the divergence angle between the twin foci increases with a larger Δn gradient. Highly birefringent PSi lenses can be designed to split light away from the element’s center, whereas less anisotropic PSiO₂ and PSiO₂/TiO₂ lenses displace a single focal spot at different polarization states, mimicking the performance of conventional birefringent lenses. We anticipate that combining these materials’ n and Δn gradients with other Si-based form factors will generate novel polarization selective elements not possible using conventional birefringent materials.

2. Optical anisotropy in porous silicon (PSi) and porous silicon oxide (PSiO₂)

The birefringence of PSi originates from its structural anisotropy [29], causing elements made from the material to exhibit polarization sensitivity. The material’s optical anisotropy becomes especially interesting in 3D GRIN optics, where the spatially varying porosity causes both index and birefringence to vary simultaneously within the element. As we previously showed, square PSi GRIN posts were shown to exhibit polarization selective lensing, making this element configuration suitable for studying how the spatially variant $\Delta n$ profile affect the anisotropic response [38]. As described in our previous work, GRIN PSi lenses focus light to a single focal point under TM polarization and produce split foci when illuminated with TE polarized light. The unique focusing behavior of these lithographically-shaped PSi lenses is a result of the four domains with orthogonal optical axes formed during porosification [38,39].

To further investigate the interplay between the birefringence profile and these GRIN lenses’ anisotropic focal response, we designed PSi square micro lenses with differing porosity gradients that correspond with varying magnitudes of $\Delta n$. The schematic in Fig. 1 depicts how these lenses’ anisotropic focal response is modified by the magnitude of the birefringence profile. In Fig. 1(a), the element is illuminated with the electric field orthogonal to all the porous domains (TM polarization). At this state, the element’s response is dictated by the ordinary refractive index (n_o) profile and is expected to generate a single focal spot because light experiences the same index profile across the four domains. At the orthogonal polarization state, light is polarized along two aligned porous domains (TE polarization), which causes the optic’s response to be governed by the extraordinary refractive index (n_e) and birefringence profiles. The three elements in Fig. 1(b) depict how elements with differing birefringence profiles focus light under TE illumination. As the magnitude of the birefringence profile increases, the divergence angle between the twin foci increases until the focus is directed away from the center of the element. In all three elements, the magnitude of refractive index profile from the element edge to the center is held constant, indicating that the divergence angle is heavily influenced by the birefringence gradient.

 

Fig. 1. (a) Cross-sectional schematic of a PSi square GRIN post under TM illumination. The coloration depicts the refractive index experienced by light polarized against the convergent porous domains. Because the electric field is not aligned along the porous domains, the refractive index profile experienced under TM illumination is uniform throughout the element volume. This results in the focusing of light to a single point. (b) Cross-sectional schematic of three PSi square GRIN lenses with increasingly larger birefringence gradients under TE illumination. The magnitude of the difference between the refractive index at the center and the edge of lens is identical for all three elements. Light polarized along the left and right porous domains experiences the extraordinary refractive index profile, causing the lens to generate two foci. As the magnitude of the birefringence increases, the two foci generated at this polarization state diverge more from the center of the element.

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Three porous materials (PSi, PSiO₂, and TiO₂-infilled PSiO₂) with varying magnitudes of birefringence were used to fabricate GRIN optics. The n_o, n_e, and Δn of the porous composites were extracted with spectroscopic ellipsometry (refractive indices for PSiO₂/TiO₂ are discussed in a latter section and in Fig. 8). PSi thin films of varying porosity were electrochemically porosified at selected current densities, while PSiO₂ and TiO₂-infilled PSiO₂ variants of these films were formed as further described in the methods section. The ellipsometric data collected from these films were fit to a uniaxial material model that extracts both n_e and n_o [42–44]. The porosity of the various films was calculated using the Bruggeman Effective Medium approximation for a two-component system (Eq. (1)).

 

Fig. 2. (a) Ordinary (n_o) and extraordinary (n_e) refractive indices as a function of porosity for PSi and PSiO₂. Filled symbols are the extraordinary index, and open symbols are the ordinary index values for both composites. (b) Birefringence (n_e-n_o) as a function of porosity, extracted from ellipsometric data. (c) Birefringence for porous silicon across visible wavelengths, showing a very large Δn > 0.3 at shorter wavelengths.

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Figure 2(b) displays the measured Δn of PSi and PSiO₂ as a function of porosity at a wavelength of 633 nm. For PSi, Δn has a maximum of 0.26 at 60% porosity and decreases quadratically toward compositions of pure Si and air. PSiO₂ exhibits similar behavior, with Δn peaking at a value of ∼0.03 with a void fraction of ∼50%. A Bruggeman effective medium approximation has been fit to the experimental data for both composites, and matches well with the experimental values [43]. At other wavelengths of the visible spectrum, the birefringence for PSi becomes even larger (Fig. 2(c)), with the Δn approaching 0.4 at shorter wavelengths and exceeding the birefringence of intrinsically anisotropic crystals like rutile titania. PSi’s large and tunable optical anisotropy, when coupled with the geometric versatility afforded by silicon processing, makes the material an interesting platform for generating GRIN elements with birefringence gradients not accessible with conventional anisotropic materials.

3. Highly birefringent porous silicon lenses

Microlenses with gradient birefringence and refractive index profiles were formed by changing the etching current density as a function of time during porosification. Figure 3 describes the anisotropic focal response of square GRIN microlenses made with highly birefringent PSi. The three elements depicted in this figure are designed with an identical index range of 0.3 (n_high-n_low=0.3) for the ordinary refractive index profile (n_o), such that the three different objectives will focus similarly under TM illumination.

 

Fig. 3. (a-b) Square GRIN lenses (greyed out region) made with refractive index profiles of identical range (∼0.3) under TM illumination (a) and TE illumination (b). The differing birefringence gradients in these elements causes the two foci produced under TE illumination to diverge light differently. (c-d) Optical thickness profiles for polarization-selective lenses with differing birefringence gradients under TM illumination (c) and TE illumination (d). All elements with identical index ranges have a parabolic optical thickness profile under TM mode illumination. The degree of divergence between these lenses’ twin foci is determined by the birefringence gradient applied during formation. The two foci diverge more greatly as the birefringence gradient increases. (e) Ordinary (n_o) and extraordinary (n_e) refractive index profiles for these GRIN lenses. (f) Spatially changing birefringence gradients used in the formation of these elements.

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The ordinary and extraordinary refractive indices extracted for the porous composites are used to predict the optical thickness profile for these elements, with the Δn coupled spatially with the n_o profile to account for the porosity dependent birefringence. Much like our previous work on square GRIN lenses, the optical thickness (OPT) at the transverse magnetic (TM) and transverse electric (TE) polarization states are described by Eqs. (2) and 3 [38]:

Table 1. Birefringence Coefficients Relating Δn to n_o for PSi and PSiO₂

View Table

As described in our previous work, GRIN lenses under TM illumination will have a quadratic optical thickness profile because of the orthogonal alignment of the electric field with respect to all four pore domains. For lenses characterized under TE illumination, the optical thickness is now additionally influenced by the spatial birefringence profile used to generate the GRIN. Whereas a constant birefringence of 0.15 was previously assumed for these GRIN elements, our parametric study of PSi and PSiO₂’s anisotropic refractive indices reveals how Δn gradients can be tuned to engineer the split focusing behavior. The following discussion will describe how these three optically anisotropic porous composites modify the beam splitting focal response as a function of the Δn gradient.

Three different elements with an identical ordinary index (n_o) range of 0.3 were fabricated, with the first element having an n_center to n_edge of 1.55 to 1.25, the second from 1.8 to 1.5, and the last element having a range from 2.1 to 1.8. Keeping the range of the n_o profile identical is necessary to contrast the consistent focal behavior of these lenses under TM illumination with the highly variable response under TE illumination. At TM illumination, all elements focus to a back focal length of ∼12 µm, yielding a lens with a numerical aperture of ∼0.5 (Fig. 3(a)) (Fig. 6 shows the all the experimental and simulated (COMSOL) TM and TE mode X-Z intensity scans for the elements shown in Fig. 3). Figure 3(b) shows the focal responses in X-Z under TE illumination. Under this polarization state, the optic splits an incoming beam into twin foci, with the divergence angle between the output beams becoming larger as the magnitude of the Δn gradient increases. When the square lens is fabricated with a smaller Δn gradient, the focal scan depicts two foci that bend inward towards the center of the element. At an intermediate Δn gradient, the twin foci emerge in parallel, mimicking the behavior of two smaller adjacent parabolic lenses. The final GRIN lens (n_range=2.1 to 1.8) contains a Δn gradient that is twice the magnitude of that used for the previous lens (n_range=1.8 to 1.5). In this case, the divergence angle between the foci increases further, producing two beams splitting away from the center of the element.

These lenses’ polarization-dependent focal behavior is predicted by the optical thickness profiles shown in Figs. 3(c) and 3(d). The lens under TM mode illumination will converge an incoming beam into a single focal spot, which is supported by the parabolic shape of its optical thickness profile. Given the identical magnitude of the n_o profile and the identical TM focal responses shown in Fig. 6, all three lenses should also have the same OPT profile at this polarization state. The OPT profile under TE illumination is more complex and is defined by the interaction of polarized light with domains containing spatially varying birefringence. For lenses made with highly birefringent PSi, the focal response manifests as twin foci that either converge towards the center or diverge away from the lens depending on the magnitude of the Δn gradient. Figure 2 showed that n_e and Δn change nonlinearly with respect to n_o, meaning that the element’s response under TE illumination will not be constant even if the n_o profile is identical for different devices. Figure 3(d) shows the OPT profile for GRIN lenses made with increasingly larger birefringence from left to right. The OPT manifests as two adjacent parabolic lenses wherein the rotation of each lens’s axis is modified by the magnitude of the Δn gradient. When the lens has a low Δn, the profile shows two parabolic lenses rotated towards the center, supporting the observed intensity scan in Fig. 3(b) that depicts two foci directed towards the center of the lens. When an intermediate Δn gradient is applied, its OPT profile shows two parabolas focusing in parallel. Finally, at a high Δn, the two parabolic OPT profiles within the lens are rotated away from the center of the element. The OPT profiles of these three lenses support the behavior displayed in their corresponding X-Z intensity scans in Fig. 3(b).

Figures 3(e) and 3(f) compare the refractive index (n_o and n_e) and the birefringence (Δn) profiles for the three PSi GRIN lenses. The black trace represents the element with the lowest Δn gradient (Δn_range∼0.01, n_range=1.55 to 1.25), the red trace represents the element with an intermediate Δn gradient (Δn_range>0.01, n_range=1.8 to 1. 5), and the blue trace represents the element with a large Δn gradient (Δn_range>0.03, n_range=2.1 to 1.8). Both figures depict the nonlinearity of the n_e and Δn profiles across elements made with linear n_o profiles and underscore the importance of understanding the material’s variable anisotropy when designing polarization-sensitive elements where one can simultaneously define geometry and index profile.

4. Structurally anisotropic porous silicon oxide lenses

PSiO₂ retains the anisotropic porous structure of PSi after thermal oxidation. The measured refractive indices of PSiO₂ in Fig. 2 reveals that the material’s Δn still changes nonlinearly with n_o even though its birefringence is significantly lower than PSi. Thus, PSiO₂ GRIN lenses will also feature a polarization-dependent focal response defined by the material’s spatially variant Δn, albeit to a lesser degree than what is attainable before thermal oxidation.

Figure 4(a) shows the X-Z focal scan of a PSiO₂ lens under TM and TE illumination. Under TM illumination, the lens focuses a beam to a focal length of ∼30 µm, a response generated by the element’s very shallow refractive index range of 0.1 (n_range=1.2 to 1.1, center to edge). At the orthogonal TE polarization state, instead of producing two distinct foci as observed with highly birefringent PSi GRIN lenses, the element generates a single focal spot at a focal length of ∼40 µm. The change in focal length observed between TM and TE polarization means that the element is still birefringent. However, the material’s significantly lower Δn causes the twin parabolas of its optical thickness profile to rotate more sharply towards the center, effectively producing a single focal spot with a working distance that differs from the TM mode response. This bifocusing behavior effectively mimics the behavior shown by birefringent lenses cut from inorganic crystals like quartz or calcite. Figure 7 shows a comparison of the experimental and simulated (COMSOL) anisotropic focal responses of the lenses in Fig. 4 under TM and TE mode illumination.

 

Fig. 4. (a) A GRIN lens made from PSiO₂, which is an order of magnitude less birefringent than PSi. The low birefringence results in only a small change in the focal length between the two polarization states. (b) PSiO₂/TiO₂ GRIN lenses demonstrate that infiltrating the structure with TiO₂ shortens the focal length of the PSiO₂ lens and reduces the change of the anisotropic response due to the lower birefringence of PSiO₂/TiO₂. (c) Ordinary (n_o) and extraordinary (n_e) refractive index profiles for these oxidized GRIN lenses. (d) Spatially changing birefringence gradients used in the formation of these elements. The addition of 5 layers of TiO₂ via ALD in the pores reverses the directionality of the birefringence gradient from the center to the edge.

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Figure 4(b) shows the X-Z focal scan of a PSiO₂/TiO₂ lens, which is made by infiltrating the pores of the PSiO₂ element shown in Fig. 4(a) with TiO₂ via atomic layer deposition (ALD). The infiltration of porous GRIN composites with secondary materials is a strategy used to increase the material’s effective refractive index and has been used to change the spectral response of optical superlattices made with PSiO₂ [44]. For this microscale GRIN device, the pores are filled with 5 layers of TiO₂ via ALD, which changes the element’s refractive index and birefringence profiles. The optical constants for PSiO₂/TiO₂ filled with 5 and 10 layers of TiO₂ are shown in Fig. 8(a), while Fig. 8(b) displays the birefringence for this composite at different increments of infilling.

Coating the surface of the pores with TiO₂, increases the element’s n_o and n_e profiles (n_range=1.42 to 1.26), which decreases the focal length of the PSiO₂ lens from ∼30 µm to ∼17 µm under TM illumination. Under TE illumination, the element produces a single focal spot at a focal length of ∼20 µm. While the low birefringence of PSiO₂/TiO₂ caused this element’s focal response to behave similarly with the PSiO₂ lens in Fig. 4(a), the smaller change in focal length between the two polarization states can be explained the different Δn gradients of PSiO₂ and PSiO₂/TiO₂. When PSiO₂ is conformally coated with a few layers of TiO₂, the birefringence of the material decreases, here increasing from center to edge as shown by the refractive index and birefringence profiles shown in Fig. 4(c) and 4(d). This effectively reduces the birefringence of the element and TE response to have a shallower profile that gives rise to the similar focal response between both polarization states. This finding suggests that infiltrating a porous GRIN element with secondary material provides an additional means to change both the refractive index and the birefringence of these porous composites.

5. Conclusion

This study demonstrates how the spatially variant birefringence profiles of PSi-based porous composites affect the polarization selective focal responses of GRIN elements. The birefringent refractive indices of PSi, PSiO₂, and PSiO₂/TiO₂ were experimentally measured and used to design GRIN lenses with varying magnitudes of optical anisotropy. Highly birefringent PSi lenses demonstrate pronounced tunability of the anisotropic response when illuminated by TE polarized light. We show that the divergence angle between the generated twin foci become larger when the magnitude of the birefringence gradient increases while the index range is held constant. Conversely, when the same elements are made with less anisotropic materials like PSiO₂ and PSiO₂/TiO₂, the degree of splitting between foci is so low that the lenses merely displace a single focal spot at opposite polarization states. Depositing a transparent, high refractive index material like TiO₂ into the pores of these GRIN devices introduces an additional approach for modifying the PSiO₂ GRIN lens’ focal response. Finite element COMSOL simulations of these micro-optics’ birefringent response support our experimentally measured optical intensity distributions. The results shown demonstrate the importance of considering the spatially variant birefringence when designing 3D GRIN optics with structurally birefringent materials.

6. Experimental section

6.1 Silicon microelement fabrication

Fabrication was performed on 4 in. diameter, degenerately doped (ρ∼0.001 to 0.005 Ω-cm) p-type Si wafers (Topsil). Wafers were rinsed successively in acetone, isopropyl alcohol, DI water, and isopropyl alcohol, and dried under a stream of nitrogen gas. The wafer was then descummed for 2 minutes in a March Jupiter III RIE parallel plate reactive ion etcher operating at 100 W with a gas flow containing a 2:1 ratio of oxygen:H₂/Ar gas. A 1.0 µm SiO₂ diffusion barrier was deposited onto the backside of the wafer via plasma-enhanced chemical vapor deposition (Trion Minilock-Orion PECVD System). N-type doping was performed in a phosphorus diffusion furnace at 1000°C for 10 minutes, followed by dissolution of the backside SiO₂ diffusion barrier by immersing the wafer in 48 wt% aqueous hydrofluoric acid. Microelements were patterned by depositing SPR220-4.5 (Shipley) positive photoresist under manufacturer recommended conditions and exposing with an EVG620 mask aligner (EV Group) using an energy dose of 220 mJ/cm². The patterned photoresist was developed in a solution containing 5:1 H₂O: AZ 400 K Developer for 35-40 seconds before a 15 second immersion in 10:1 H₂O: AZ 400 K Developer to rinse off any remaining exposed polymer. Si etching was performed with a Pegasus ICP-DRIE (SPTS Technologies) running a Bosch process. The wafer was submerged in photoresist stripper for 5 minutes, and rinsed successively in acetone, isopropyl alcohol, DI water, and isopropyl alcohol before drying under nitrogen gas. The Si wafer is cleaved in into 1-inch squares containing arrays of the microelements and placed into an electrochemical cell for porosification.

6.2 Porous silicon etching

Etching was performed in a polypropylene cell with an exposed etch area of ∼1.20 cm². Prior to etching, the diced silicon wafers were rinsed in acetone and isopropyl alcohol and dried under a stream of nitrogen. Contact to the back of the Si wafer was established with a stainless-steel electrode. The electrolyte was comprised of a 1:1 volume ratio of 49% hydrofluoric acid (aq) (J.T. Baker) and 100% ethanol (Decon Labs). A 5 mm diameter Pt-Ir inoculating loop (Thomas Scientific) served as the counter electrode and was located at the center of the cell ∼25 mm from the etch surface to provide a uniform current density across the sample. Current was delivered to the cell by a SP-200 Research Grade Potentiostat/Galvanostat (Bio-Logic Science Instruments). The current waveforms for generating refractive index gradients were constructed via BenchLink Waveform Builder Pro software (Keysight Technologies, Inc.) and sent to the SP-200 through a 33220A Function/Arbitrary Waveform Generator (Keysight Technologies, Inc.). After etching, all structures were thoroughly rinsed with ethanol and dried under a stream of nitrogen. Elements were characterized after mechanically transferring them onto a glass substrate.

6.3 Thermal oxidation

PSi samples were laid onto a quartz plate and loaded into a Lindberg Hevy-Duty Lancer M-300 oxidation tube furnace with MFC gas flow controls for oxygen and nitrogen gases. Under N₂ flow set to 8 sccm in the MFC controller, the temperature of the furnace was increased from 400 °C to 925 °C. Upon reaching the oxidation temperature, the N₂ gas flow was switched off and replaced with O₂ gas at a flow rate of 8 sccm and held for 45 minutes to convert PSi to PSiO₂. After oxidation, the O₂ flow was switched off and N₂ was reintroduced into the furnace until the samples cooled sufficiently for retrieval.

6.4 TiO₂ ALD deposition

The ALD system (Cambridge Nanotech) used water and tetrakis(dimethylamido)titanium as precursors for TiO₂ deposition, and was carried out at a chamber temperature of 140°C. This recipe, developed with the assistance of Cambridge Nanotech, used (for both precursors) a stop valve opening time of 0.3 s, precursor pulse time of 180 s, and a precursor dwell time of 180 s.

6.5 Optical characterization

Optical spectra for PSi and PSiO₂ films were taken on a J.A. Woollam VASE ellipsometer. Spectroscopic ellipsometry data and oblique incidence reflectance were measured between 400 to 1100 nm at incident angles of 45°, 65° and 75°. Refractive index dispersions were extracted from ellipsometric and reflectance data using a biaxial Cauchy fit included in the J.A. Woollam software.

6.6 XZ confocal imaging

A WITec alpha 300 S upright confocal microscope fit with a 100x Zeiss Epiplan-Apochromat objective (NA 0.95) was used to perform X-Z plane optical intensity depth scans of the square GRIN lenses. A HeNe laser (633 nm) was used for plane wave illumination. The beam was then spatially filtered and collimated and a linear polarizer and half-wave plate are placed in the optical rail to control polarization. The light source was directed through the sample and collected by the objective. A 25-µm, 0.1 NA multimode fiber transmits the collected photons to a silicon photomultiplier tube. The multimode fiber acts as a pinhole in the confocal setup, enabling the collection of light at discrete pixels that build up the intensity scan. Confocal scanning is performed by using a piezo actuated 2-axis stage with nanometric lateral resolution to image in the x and y directions, and a stepper motor with 50 nm resolution to obtain the optical profile in Z. The dimension of the optical scan is adjusted such that the scan width exceeds the sample width by 5 µm on either side and steps the pixels in increments of 50 nm in the x direction and 50 nm in the z direction. This oversamples the intensity distribution and resolves the features of the intensity scan projected into the far field. Photons are collected over a 10 ms integration time, and the light sources are adjusted with a neutral density filter to constrain the illuminating intensity within the linear range of the photon counting regime.

7. Appendix figures

 

Fig. 5. (a) Absorption coefficient of PSi containing 65% (red) and 80% (black) void volume fractions, representing the lowest and highest porosities used for fabricating GRIN lenses (determined via ellipsometry). (b) Porosity of PSi and PSiO₂ as a function of current density applied during the material’s electrochemical formation. Data in (b) is used to guide the design of porosity gradients for 3D GRIN elements.

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Fig. 6. A comparison of the experimentally measured and simulated X-Z intensity scans from PSi GRIN lenses with identical refractive index range (n_center-n_edge=0.3). Experimental and simulated (COMSOL) intensity scans compare the focal response for polarization selective lenses for elements designed with (a-b) n_center= 1.55 and n_edge=1.25, (c-d) n_center= 1.80 and n_edge=1.55, and (e-f) n_center= 2.1 and n_edge=1.80.

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Fig. 7. A comparison of the experimentally measured and simulated X-Z intensity scans for PSiO₂ GRIN lenses. (a) The top row of lenses shows a PSiO₂ GRIN lens with a focal length of 40 µm under TM illumination, and 50 µm under TE illumination. (b) The bottom row shows that adding TiO₂ into the pores via ALD increases the index and shortens the focal length to ∼17 µm, with very little change (∼2 µm) in the focal length under TE illumination.

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Fig. 8. (a) Change in the refractive index of PSiO₂ when infiltrated with TiO₂ via ALD. (b) Birefringence of PSiO₂/TiO₂ at different levels of TiO₂ loading. The composite’s birefringence shows a trend of decreasing with higher levels of TiO₂ loading.

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Funding

U.S. Department of Energy (DE-SC0001293, DE-SC0019140).

Acknowledgements

The authors thank G. Mensing and J. Maduzia at the Micro-Nano-Mechanical Systems Cleanroom (University of Illinois at Urbana-Champaign) for assistance with process development. This work was supported by the U.S. Department of Energy “Light-Material Interactions in Energy Conversion” Energy Frontier Research Center under grant DE-SC0001293, the U.S. Department of Energy “Photonics at Thermodynamic Limits” Energy Frontier Research Center under grant DE-SC0019140, and the University of Illinois at Urbana-Champaign. This work was carried out in part in the Materials Research Laboratory Central Facilities, University of Illinois.

Disclosures

The authors declare no conflict of interest.

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